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What is the time complexity for deleting a key or integer in Van Emde Boas data structure?

(a) O (log M!)

(b) O (log (log M))

(c) O (M!)

(d) O (M^2)

My question is taken from Trees in division Trees of Data Structures & Algorithms I

I had been asked this question in homework.

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The correct option is (b) O (log (log M))

For explanation: In order to delete a key or integer in the Van Emde Boas data structure, the operation can be performed on an associative array. Hence, the time complexity for deleting a key or integer in Van Emde Boas data structure is O (log (log M)).

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